Question 1

Divide: $$\frac { 5 x - 3 } { 3 x - 2 } \div \frac { 25 x - 15 } { 21 x - 14 }$$

Accepted Answer

A)  $\frac { 5 } { 7 x }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 5 ( 5 x - 3 ) ^ { 2 } } { 7 ( 3 x - 2 ) ^ { 2 } }$ 
D)  $\frac { 5 ( 5 x - 3 ) } { 7 ( 3 x - 2 ) }$ 
E)  $\frac { 7 } { 5 }$ 
A)  $\frac { 5 } { 7 x }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 5 ( 5 x - 3 ) ^ { 2 } } { 7 ( 3 x - 2 ) ^ { 2 } }$ 
D)  $\frac { 5 ( 5 x - 3 ) } { 7 ( 3 x - 2 ) }$ 
E)  $\frac { 7 } { 5 }$

Question 2

Multiply the expressions, and simplify the results. Assume there are no zero denominators. $$x ( x + 3 ) \left( \frac { 2 } { x } + \frac { 1 } { x + 3 } \right)$$

Accepted Answer

A)  $3 x ^ { 2 } + 6$ 
B)  $3 x + 6$ 
C)  $4 x + 6$ 
D)  $3 x + 7$ 
E)  $9$ 
A)  $3 x ^ { 2 } + 6$ 
B)  $3 x + 6$ 
C)  $4 x + 6$ 
D)  $3 x + 7$ 
E)  $9$

Question 3

Multiply the expressions, and simplify the results. Assume there are no zero denominators. $$6 x ^ { 2 } \left( \frac { 2 } { 3 x ^ { 2 } } + \frac { 1 } { 6 } \right)$$

Accepted Answer

A)  $4 + x ^ { 2 }$ 
B)  $5 x ^ { 2 }$ 
C)  $4$ 
D)  $x ^ { 2 }$ 
E)  $5 x ^ { 4 } + x ^ { 2 }$ 
A)  $4 + x ^ { 2 }$ 
B)  $5 x ^ { 2 }$ 
C)  $4$ 
D)  $x ^ { 2 }$ 
E)  $5 x ^ { 4 } + x ^ { 2 }$

Question 4

Simplify. Assume there are no zero denominators. $$\frac { 4 - 2 x } { 6 x - 12 }$$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  3 
C)  $- \frac { 1 } { 3 }$ 
D)  $- 3$ 
E)  Does not simplify. 
A)  $\frac { 1 } { 3 }$ 
B)  3 
C)  $- \frac { 1 } { 3 }$ 
D)  $- 3$ 
E)  Does not simplify.

Question 5

Simplify. Assume there are no zero denominators. $$\frac { 3 x - 6 } { 3 - x }$$

Accepted Answer

A)  $2 x - 2$ 
B)  x = 3 
C)  x = 2 
D)  3 
E)  Does not simplify. 
A)  $2 x - 2$ 
B)  x = 3 
C)  x = 2 
D)  3 
E)  Does not simplify.

Question 6

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches -7. $$y = \frac { x + 8 } { ( x + 7 ) ( x - 8 ) }$$

Accepted Answer

A)  Y approaches $+ \infty$ from the left and $- \infty$ from the right. 
B)  Y approaches $- \infty$ from the left and $+ \infty$ from the right. 
C)  Y approaches $- 8$ from the left and $8$ from the right. 
D)  Y approaches $8$ from the left and $- 8$ from the right. 
E)  Y approaches $\infty$ from the left and $8$ from the right. 
A)  Y approaches $+ \infty$ from the left and $- \infty$ from the right. 
B)  Y approaches $- \infty$ from the left and $+ \infty$ from the right. 
C)  Y approaches $- 8$ from the left and $8$ from the right. 
D)  Y approaches $8$ from the left and $- 8$ from the right. 
E)  Y approaches $\infty$ from the left and $8$ from the right.

Question 7

The current, I, in an electrical circuit is found by dividing the voltage, V, by the resistance, R. Suppose the voltage and resistance vary with time as in the following equations. $$V = \frac { t ^ { 2 } - 25 } { 2 t ^ { 2 } - 9 t - 5 } \text { and } R = \frac { t + 5 } { t ^ { 2 } }$$ Assume there are no zero denominators. Find a formula in terms of t that gives the current, I.

Accepted Answer

A)  $I = \frac { t ^ { 2 } } { 2 t + 1 }$ 
B)  $I = \frac { 2 t + 1 } { t ^ { 2 } }$ 
C)  $I = \frac { t ^ { 2 } } { 2 t - 1 }$ 
D)  $I = \frac { t ^ { 2 } } { 2 t - 9 t - 5 }$ 
E)  $I = \frac { t ^ { 2 } - 25 } { 2 t + 9 }$ 
A)  $I = \frac { t ^ { 2 } } { 2 t + 1 }$ 
B)  $I = \frac { 2 t + 1 } { t ^ { 2 } }$ 
C)  $I = \frac { t ^ { 2 } } { 2 t - 1 }$ 
D)  $I = \frac { t ^ { 2 } } { 2 t - 9 t - 5 }$ 
E)  $I = \frac { t ^ { 2 } - 25 } { 2 t + 9 }$

Question 8

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $ \frac{\text { 5900 feet  } }{\text {  1200 feet per second } } $

Accepted Answer

A)  5.92 seconds 
B)  4.42 seconds 
C)  5.02 seconds 
D)  4.92 seconds 
E)  4.87 seconds 
A)  5.92 seconds 
B)  4.42 seconds 
C)  5.02 seconds 
D)  4.92 seconds 
E)  4.87 seconds

Question 9

Find the missing number or expression in each pair of equivalent fractions. Assume there is no zero denominators. $$\frac { 30 } { 7 } , \frac { ? } { 28 }$$

Accepted Answer

A)  $119$ 
B)  $121$ 
C)  $118$ 
D)  $120$ 
E)  $122$ 
A)  $119$ 
B)  $121$ 
C)  $118$ 
D)  $120$ 
E)  $122$

Question 10

What is the least common denominator for the set of rational expressions? $$\frac { 4 } { 15 } + \frac { 19 } { 27 }$$

Accepted Answer

A)  15 
B)  270 
C)  135 
D)  27 
E)  150 
A)  15 
B)  270 
C)  135 
D)  27 
E)  150

Question 11

Simplify: $\frac { 11 } { r } + \frac { 9 } { 19 r }$

Accepted Answer

A)  $\frac { 182 } { 19 r }$ 
B)  $\frac { 200 } { 19 r }$ 
C)  $\frac { 218 } { 19 r }$ 
D)  $\frac { 109 } { 10 r }$ 
E)  $\frac { 218 } { 19 r ^ { 2 } }$ 
A)  $\frac { 182 } { 19 r }$ 
B)  $\frac { 200 } { 19 r }$ 
C)  $\frac { 218 } { 19 r }$ 
D)  $\frac { 109 } { 10 r }$ 
E)  $\frac { 218 } { 19 r ^ { 2 } }$

Question 12

Find the missing number or expression in the pair of equivalent fractions. Assume that all denominators are nonzero. $$\frac { a - 5 } { a + 5 } , \frac { ? } { a ^ { 2 } + 10 a + 25 }$$

Accepted Answer

A)  $a ^ { 2 } - 5$ 
B)  $a ^ { 2 } + 25$ 
C)  $a ^ { 2 } + 5$ 
D)  $a ^ { 2 } - 25$ 
E)  $a ^ { 2 } - 20$ 
A)  $a ^ { 2 } - 5$ 
B)  $a ^ { 2 } + 25$ 
C)  $a ^ { 2 } + 5$ 
D)  $a ^ { 2 } - 25$ 
E)  $a ^ { 2 } - 20$

Question 13

Simplify: $$\frac { 5 } { t k } - \frac { 3 } { t k }$$

Accepted Answer

A)  $\frac { 2 } { t k }$ 
B)  $- \frac { 2 } { t k }$ 
C)  $\frac { 2 } { t ^ { 2 } }$ 
D)  $2 t k$ 
E)  $\frac { 15 } { t k }$ 
A)  $\frac { 2 } { t k }$ 
B)  $- \frac { 2 } { t k }$ 
C)  $\frac { 2 } { t ^ { 2 } }$ 
D)  $2 t k$ 
E)  $\frac { 15 } { t k }$

Question 14

Simplify $$\frac { 69 \mathrm { in } ^ { 3 } } { 3 \mathrm { in } . }$$

Accepted Answer

A)  3 in2 
B)  66 in2 
C)  21 in2 
D)  23 in. 
E)  23 in2 
A)  3 in2 
B)  66 in2 
C)  21 in2 
D)  23 in. 
E)  23 in2

Question 15

Find the slope of the line connecting the points. Simplify to eliminate fractions from the numerators and denominators. $$\left( - \frac { b } { 2 } , a \right) , \left( 3 b , \frac { a } { 2 } \right)$$

Accepted Answer

A)  $- \frac { a } { 7 b }$ 
B)  $- \frac { 7 a } { b }$ 
C)  $- \frac { a } { 13 b }$ 
D)  $- \frac { 13 a } { b }$ 
E)  $- \frac { a } { 3 b }$ 
A)  $- \frac { a } { 7 b }$ 
B)  $- \frac { 7 a } { b }$ 
C)  $- \frac { a } { 13 b }$ 
D)  $- \frac { 13 a } { b }$ 
E)  $- \frac { a } { 3 b }$

Question 16

Simplify: $$\frac { t } { t + 8 } - \frac { 3 } { t + 8 }$$

Accepted Answer

A)  $\frac { t - 3 } { t - 8 }$ 
B)  $1 - \frac { 3 } { t + 8 }$ 
C)  $\frac { t - 3 } { t + 8 }$ 
D)  $\frac { 3 t } { t + 8 }$ 
E)  $\frac { t + 3 } { t + 8 }$ 
A)  $\frac { t - 3 } { t - 8 }$ 
B)  $1 - \frac { 3 } { t + 8 }$ 
C)  $\frac { t - 3 } { t + 8 }$ 
D)  $\frac { 3 t } { t + 8 }$ 
E)  $\frac { t + 3 } { t + 8 }$

Question 17

Simplify. Assume there are no zero denominators. $$\frac { 3 x - 6 } { x - 2 }$$

Accepted Answer

A)  $2 x - 3$ 
B)  x = 3 
C)  x = 2 
D)  3 
E)  Does not simplify. 
A)  $2 x - 3$ 
B)  x = 3 
C)  x = 2 
D)  3 
E)  Does not simplify.

Question 18

Solve: $$\frac { 3 } { 2 x - 7 } = \frac { 6 } { 3 x + 8 }$$

Accepted Answer

A)  $- \frac { 22 } { 7 }$ 
B)  $\frac { 22 } { 7 }$ 
C)  22 
D)  -23 
E)  23 
A)  $- \frac { 22 } { 7 }$ 
B)  $\frac { 22 } { 7 }$ 
C)  22 
D)  -23 
E)  23

Question 19

What may be concluded about these fractions? $$- \frac { b } { c } , \frac { - b } { c } , \frac { b } { - c }$$

Accepted Answer

A)  They are equal. 
B)  They are not equal. 
A)  They are equal. 
B)  They are not equal.

Question 20

Set up and solve an equation. Round to the nearest tenth. One door can clear a theater in 6 minutes. A second door can clear a theater in 9 minutes. How fast can the theater be cleared if both doors are available?

Accepted Answer

A)  15 min 
B)  0.3 min 
C)  4.6 min 
D)  3.6 min 
E)  14 min 
A)  15 min 
B)  0.3 min 
C)  4.6 min 
D)  3.6 min 
E)  14 min

Divide: $\frac { 5 x - 3 } { 3 x - 2 } \div \frac { 25 x - 15 } { 21 x - 14 }$

Multiply the expressions, and simplify the results. Assume there are no zero denominators. $x ( x + 3 ) \left( \frac { 2 } { x } + \frac { 1 } { x + 3 } \right)$

Multiply the expressions, and simplify the results. Assume there are no zero denominators. $6 x ^ { 2 } \left( \frac { 2 } { 3 x ^ { 2 } } + \frac { 1 } { 6 } \right)$

Simplify. Assume there are no zero denominators. $\frac { 4 - 2 x } { 6 x - 12 }$

Simplify. Assume there are no zero denominators. $\frac { 3 x - 6 } { 3 - x }$

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches -7. $y = \frac { x + 8 } { ( x + 7 ) ( x - 8 ) }$

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $\frac{\text { 5900 feet } }{\text { 1200 feet per second } }$

Find the missing number or expression in each pair of equivalent fractions. Assume there is no zero denominators. $\frac { 30 } { 7 } , \frac { ? } { 28 }$

What is the least common denominator for the set of rational expressions? $\frac { 4 } { 15 } + \frac { 19 } { 27 }$

Simplify: $\frac { 11 } { r } + \frac { 9 } { 19 r }$

Find the missing number or expression in the pair of equivalent fractions. Assume that all denominators are nonzero. $\frac { a - 5 } { a + 5 } , \frac { ? } { a ^ { 2 } + 10 a + 25 }$

Simplify: $\frac { 5 } { t k } - \frac { 3 } { t k }$

Simplify $\frac { 69 \mathrm { in } ^ { 3 } } { 3 \mathrm { in } . }$

Find the slope of the line connecting the points. Simplify to eliminate fractions from the numerators and denominators. $\left( - \frac { b } { 2 } , a \right) , \left( 3 b , \frac { a } { 2 } \right)$

Simplify: $\frac { t } { t + 8 } - \frac { 3 } { t + 8 }$

Simplify. Assume there are no zero denominators. $\frac { 3 x - 6 } { x - 2 }$

Solve: $\frac { 3 } { 2 x - 7 } = \frac { 6 } { 3 x + 8 }$

What may be concluded about these fractions? $- \frac { b } { c } , \frac { - b } { c } , \frac { b } { - c }$

Set up and solve an equation. Round to the nearest tenth. One door can clear a theater in 6 minutes. A second door can clear a theater in 9 minutes. How fast can the theater be cleared if both doors are available?

Algebraic Representations

Operations With Real Numbers

Solving Equations

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Formulas, Functions, Linear Equations, and Inequalities in Two Variables

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Exam 9: Rational Expressions

Divide: 5x−33x−2÷25x−1521x−14\frac { 5 x - 3 } { 3 x - 2 } \div \frac { 25 x - 15 } { 21 x - 14 }3x−25x−3​÷21x−1425x−15​

Multiply the expressions, and simplify the results. Assume there are no zero denominators. x(x+3)(2x+1x+3)x ( x + 3 ) \left( \frac { 2 } { x } + \frac { 1 } { x + 3 } \right)x(x+3)(x2​+x+31​)

Multiply the expressions, and simplify the results. Assume there are no zero denominators. 6x2(23x2+16)6 x ^ { 2 } \left( \frac { 2 } { 3 x ^ { 2 } } + \frac { 1 } { 6 } \right)6x2(3x22​+61​)

Simplify. Assume there are no zero denominators. 4−2x6x−12\frac { 4 - 2 x } { 6 x - 12 }6x−124−2x​

Simplify. Assume there are no zero denominators. 3x−63−x\frac { 3 x - 6 } { 3 - x }3−x3x−6​

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches -7. y=x+8(x+7)(x−8)y = \frac { x + 8 } { ( x + 7 ) ( x - 8 ) }y=(x+7)(x−8)x+8​

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. 5900 feet 1200 feet per second \frac{\text { 5900 feet } }{\text { 1200 feet per second } } 1200 feet per second 5900 feet ​

Find the missing number or expression in each pair of equivalent fractions. Assume there is no zero denominators. 307,?28\frac { 30 } { 7 } , \frac { ? } { 28 }730​,28?​

What is the least common denominator for the set of rational expressions? 415+1927\frac { 4 } { 15 } + \frac { 19 } { 27 }154​+2719​

Simplify: 11r+919r\frac { 11 } { r } + \frac { 9 } { 19 r }r11​+19r9​

Find the missing number or expression in the pair of equivalent fractions. Assume that all denominators are nonzero. a−5a+5,?a2+10a+25\frac { a - 5 } { a + 5 } , \frac { ? } { a ^ { 2 } + 10 a + 25 }a+5a−5​,a2+10a+25?​

Simplify: 5tk−3tk\frac { 5 } { t k } - \frac { 3 } { t k }tk5​−tk3​

Simplify 69in33in.\frac { 69 \mathrm { in } ^ { 3 } } { 3 \mathrm { in } . }3in.69in3​

Find the slope of the line connecting the points. Simplify to eliminate fractions from the numerators and denominators. (−b2,a),(3b,a2)\left( - \frac { b } { 2 } , a \right) , \left( 3 b , \frac { a } { 2 } \right)(−2b​,a),(3b,2a​)

Simplify: tt+8−3t+8\frac { t } { t + 8 } - \frac { 3 } { t + 8 }t+8t​−t+83​

Simplify. Assume there are no zero denominators. 3x−6x−2\frac { 3 x - 6 } { x - 2 }x−23x−6​

Solve: 32x−7=63x+8\frac { 3 } { 2 x - 7 } = \frac { 6 } { 3 x + 8 }2x−73​=3x+86​

What may be concluded about these fractions? −bc,−bc,b−c- \frac { b } { c } , \frac { - b } { c } , \frac { b } { - c }−cb​,c−b​,−cb​

Set up and solve an equation. Round to the nearest tenth. One door can clear a theater in 6 minutes. A second door can clear a theater in 9 minutes. How fast can the theater be cleared if both doors are available?

Algebraic Representations

Operations With Real Numbers

Solving Equations

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Filters

Divide: $\frac { 5 x - 3 } { 3 x - 2 } \div \frac { 25 x - 15 } { 21 x - 14 }$

Multiply the expressions, and simplify the results. Assume there are no zero denominators. $x ( x + 3 ) \left( \frac { 2 } { x } + \frac { 1 } { x + 3 } \right)$

Multiply the expressions, and simplify the results. Assume there are no zero denominators. $6 x ^ { 2 } \left( \frac { 2 } { 3 x ^ { 2 } } + \frac { 1 } { 6 } \right)$

Simplify. Assume there are no zero denominators. $\frac { 4 - 2 x } { 6 x - 12 }$

Simplify. Assume there are no zero denominators. $\frac { 3 x - 6 } { 3 - x }$

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches -7. $y = \frac { x + 8 } { ( x + 7 ) ( x - 8 ) }$

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $\frac{\text { 5900 feet } }{\text { 1200 feet per second } }$

Find the missing number or expression in each pair of equivalent fractions. Assume there is no zero denominators. $\frac { 30 } { 7 } , \frac { ? } { 28 }$

What is the least common denominator for the set of rational expressions? $\frac { 4 } { 15 } + \frac { 19 } { 27 }$

Simplify: $\frac { 11 } { r } + \frac { 9 } { 19 r }$

Find the missing number or expression in the pair of equivalent fractions. Assume that all denominators are nonzero. $\frac { a - 5 } { a + 5 } , \frac { ? } { a ^ { 2 } + 10 a + 25 }$

Simplify: $\frac { 5 } { t k } - \frac { 3 } { t k }$

Simplify $\frac { 69 \mathrm { in } ^ { 3 } } { 3 \mathrm { in } . }$

Find the slope of the line connecting the points. Simplify to eliminate fractions from the numerators and denominators. $\left( - \frac { b } { 2 } , a \right) , \left( 3 b , \frac { a } { 2 } \right)$

Simplify: $\frac { t } { t + 8 } - \frac { 3 } { t + 8 }$

Simplify. Assume there are no zero denominators. $\frac { 3 x - 6 } { x - 2 }$

Solve: $\frac { 3 } { 2 x - 7 } = \frac { 6 } { 3 x + 8 }$

What may be concluded about these fractions? $- \frac { b } { c } , \frac { - b } { c } , \frac { b } { - c }$